This remained the general sentiment in England for a long time. A couple of centuries later, Dr. Samuel Johnson was pontificating: “A man who has not been in Italy, is always conscious of an inferiority, from his not having seen what it is expected a man should see.”
The Shakespeare plays set in Italy (or Vienna, or Bohemia, or wherever) were about Italy etc. about as much as The Mikado was about Japan anyway. Gilbert may have known more about Japan than Shakespeare knew about the places he wrote about, but neither of them felt any need to get it right, and I don’t think their respective audiences demanded it of them (for different reasons, likely).
There wasn’t an “Italy” as a country when Shakespeare was alive. Italy didn’t become a nation until 1861 and it gained most of its current form by 1870 (it lost Trieste after WWII) There were maps available at the time and it’s probable that Shakespeare spoke with people who had actually been to the states which comprised Italy at the time.
Anyway, Shakespeare wrote his plays for people who probably didn’t know where the places he wrote about were and who almost certainly never would have traveled there during their lifetimes. He didn’t have to get it “right”; close was good enough.
Gilbert deliberately didn’t research much about feudal Japan in order to write The Mikado and emphasise his point (satire of Victorian England) across more strongly. I think I read somewhere that the most research he did was into the general “look” of feudal Japan (the costumes, the way people sat) and adding the “Miya sama” marching song.
From the Globe?
LOL 
Yes, but most of them were Chinese.
Of course, that was the age of the Grand Tour, and the gentry were not considered fully educated until they’d done it.
Thank you. (I, quite shamelessly, am rather proud of myself!)